(untitled) (Advances in Applied Mathematics and Mechanics, 2018)
A new scheme for the Zakharov-Kuznetsov (ZK) equation with the accuracy order of O(∆t^2+∆x+∆y^2) is proposed. The multi-symplectic conservation property of the new scheme is proved. The backward error analysis of the new multi-symplectic scheme is also implemented. The solitary wave evolution behaviors of the Zakharov-Kunetsov equation are investigated by the new multi-symplectic scheme. The accuracy of the scheme is analyzed.